From a6cb1a4029a386ba6a90f6bb4d03db1a52632797 Mon Sep 17 00:00:00 2001
From: Kevin Choi <k.choi-1@student.tudelft.nl>
Date: Fri, 1 Feb 2019 19:50:21 +0000
Subject: [PATCH] Made DOS exercise in ex. 1 simpler

---
 src/8_many_atoms.md | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/src/8_many_atoms.md b/src/8_many_atoms.md
index 8bff514..0a168e5 100644
--- a/src/8_many_atoms.md
+++ b/src/8_many_atoms.md
@@ -229,8 +229,7 @@ Recall the eigenfrequencies of a diatomic vibrating chain in the lecture notes w
 
 1. Find the magnitude of the group velocity near $k=0$ for the _acoustic_ branch.
 2. Show that the group velocity at $k=0$ for the _optical_ branch is zero.
-3. Derive an expression for the density of states $g(\omega)$ in the _optical_ branch.
-4. Make a plot of your expression of $g(\omega)$ found in 3. Does the plot look like the bar diagram of the density of states of the optical branch in the lecture notes?
+3. Derive an expression for the density of states $g(\omega)$ for the _acoustic_ branch and small $ka$. Make use of your expression of the group velocity in 1.
 
 #### Exercise 2: atomic chain with 3 different spring constants
 Suppose we have a vibrating 1D atomic chain with 3 different spring constants alternating like $\kappa_ 1$, $\kappa_2$, $\kappa_3$, $\kappa_1$, etc. All the the atoms in the chain have an equal mass $m$.
-- 
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